Definition 4 ([1]}) 
Given two agents, \(a_i\)  and \(a_j\) , who find each other acceptable, \(\operatorname{rank}(a_i,a_j)\)  is 1 plus the number of agents that \(a_i\)  prefers to \(a_j\) . For example, if \(a_3\)  has the preference list \([a_1, a_2]\) , \(\operatorname{rank}(a_3, a_1) = 1\)  and \(\operatorname{rank}(a_3, a_2) = 2\) .

